P. Němec

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math.CO2026

Note as to size-minimal hypercompletly separating systems

B. Batikova, T. J. Kepka, P. C. Nemec

If $S$ is a non-empty finite set, $∣ S ∣ = s$ , then a system $A$ of subsets of $S$ is a size-minimal hypercompletely separable system (i.e., for every $a \in S$ there are $A,B…

math.CO2025

Size-minimal combinatorial designs of staircase type

Barbora BatÃ kovÃ¡, TomÃ¡Å¡ J. Kepka, Petr C. NÄmec

Given a positive integer $n$ and a partitioning $n = r_{1} s_{1} + \dots + r_{t} s_{t}$ , $t, r_{i}, s_{i}$ positive integers, such that $r_{1} > \dots > r_{t}$ (for $t \geq 2$ ), we can write $n$ symbols $1,\dots…